## Harmonic voltage distortion

In the mains supply system, **harmonic voltage distortion** is the consequence of the flow of harmonic currents through the impedances in the power supply circuit connected to the converter. A typical power supply system at an industrial or mining plant consists of a source of AC power generation, which can either be a local generating station in a small system or a power station at the other end of a transmission line or transformer in a large system.

The impedance between the ‘ideal’ generator and the main busbar is usually referred to as the

source impedance Zsof the supply system.

Additional impedance, usually comprising cables, busbars, transformer, etc exists between the main busbar and the converter busbar and is the **cable impedance Zc**, as shown in Figure 1 below.

The flow of current to a variable speed motor is controlled by the **converter**. The current is non-sinusoidal due to the non-linearity of the converter and the generation of harmonic currents. The flow of distorted current through the power distribution and supply system produces a distorted volt drop across the source and distribution impedances in series.

Other equipment, such as electric motors or even other consumers can be connected to the main busbar. Consequently, this busbar is referred to as the **point of common coupling (PCC)**.

The voltage at the PCC will be distorted to an extent depending on the magnitude of the distorted current, the magnitude of the impedances and the ratio between them.

**If the source impedance is low, then the voltage distortion will be low.**

The distribution impedance must be calculated from the design details of the distribution system.

A high distribution impedance will tend to reduce the voltage at the point of common coupling but increase it at the converter connection terminals. This voltage distortion can cause interference with the electronic trigger circuits of the converter and give rise to other problems if it becomes too high.

If the magnitude and the frequency of each harmonic current is known,

a simple application of Ohm’s lawwill give the magnitude of each harmonic voltage and the sum of them will give the total distorted voltage.

### Total harmonic distortion (THD) of voltage and current

From AS 2279-1991 Part 2, the total harmonic distortion (THD) of voltage and current are given by the following formulae. Generally, it is sufficient to use values of **n up to 25**.

**Where:**

**V**= Total harmonic voltage distortion_{T}**I**= Total harmonic current distortion_{T}**V**= Fundamental voltage at 50 Hz_{1}**I**= Fundamental current at 50 Hz_{1}**V**= nth harmonic voltage_{n}**I**= nth harmonic current_{n}

The acceptable levels of harmonics in industrial power supply networks are clearly defined in Table 1 of the Australian standard AS 2279-1991 Part 2: disturbances in mains supply networks.

Briefly, limits are set for the level of total harmonic voltage distortion, which are acceptable at the point of common coupling (PCC).

The application of these standards requires **the prior calculation of harmonic distortion at all points in the system** before the converter equipment can be connected and, under certain circumstances, actual measurements of harmonic voltage to confirm the level of distortion.

**Reference //** Practical Variable Speed Drives and Power Electronics – Malcolm Barnes CPEng, BSc(ElecEng), MSEE, Automated Control Systems, Perth, Australia (Get this book from Amazon)

CORRECTION: Is it not that the external Z is Ze not Zs. Zs is normally Zs= Ze + R1+R2

Is it not that the external Z is Ze not Zs. Ze is normally Ze= Zs + R1+R2